by: Zeke Hausfather, Berkeley Earth

The relationship between greenhouse gas (GHG) emissions and future warming is complex, depending on the atmospheric lifetime of gases, their radiative forcing, and the thermal inertia of the Earth, particularly our oceans. Many non-CO2 GHGs have shorter atmospheric lifetimes, and the global warming-equivalent values commonly used for analysis of emission impacts fail to effectively capture important relationships between emission time and resulting impact on global surface temperature.

In order for researchers to easily translate emissions of CO2, CH4, and N2O into future warming consistent at a global level with the results obtained from the latest generation of climate models, we have developed a simple python-based climate model we call SimMod (available on github here). If provided with annual emissions of each GHG, it will convert these into atmospheric concentrations, radiative forcing, and transient climate response (warming) per year through 2100 (or any specified period).

The model comes with four built-in emission scenarios, the IPCC’s RCP scenarios that can be used as a starting point for analysis. We also used the published atmospheric concentrations, radiative forcing, and transient climate response to evaluate the model performance. The emissions scenarios are shown in Figure 1, below.


Figure 1: Emissions of CO2, CH4, and N2O for the four RCPs.


These emissions are converted into concentrations either using pulse-response functions for each gas (simple exponential decay for CH4 and N2O; a response function fit to the BERN carbon cycle model in the case of CO2) or using the BEAM carbon cycle model for CO2, whichever the user specifies. The resulting atmospheric concentrations for each RCP scenario are shown in Figure 2. In general, the modeled concentrations match RCP scenarios well, with some exceptions for high CO2 emission scenarios (e.g. RCP 8.5) where carbon cycle feedbacks reduce ocean uptake in a manner not reflected in the simple pulse response model.


Figure 2: Atmospheric concentrations CO2, CH4, and N2O for the four RCPs and SimMod, with values normalized for the year 2000. Dashed lines are SimMod results; solid lines are RCP-provided values.

Atmospheric concentrations of each gas are converted into radiative forcing using the IPCC’s simple radiative forcing functions. When provided with the same atmospheric concentrations as the RCP scenarios, the resulting radiative forcing closely matches RCP scenario forcing, as shown in Figure 3.


Figure 3: Total direct radiative forcing values (CO2 + CH4 + N2O) for the four RCPs and SimMod using the RCP-provided concentrations. Dashed lines are SimMod results; solid lines are RCP-provided values.

Finally, radiative forcing is converted into transient climate response using a continuous diffusion slab ocean model adapted from Caldeira and Myhrvold (2012) and a specified climate sensitivity. The global average temperature is estimated by a weighted average of the ocean model response and the equilibrium temperature response over land. Figure 4 shows the resulting transient temperature response given the RCP scenario forcings compared to the IPCC’s latest climate model runs (CMIP5). The black line is the multi-model mean, while the grey area is the 95% confidence intervals of climate models. The solid red line is the SimMod transient climate response, while the dashed red line represents the equilibrium response (e.g. if there were no oceans to buffer the climate response time).


Figure 4: SimMod transient (solid red) and equilibrium (dashed red) temperature response compared to CMIP5 model results for each RCP.

We hope this model provides a useful tool for researchers looking to move away from simplistic global warming potentials to examine the time-evolution of the temperature response to different emission or mitigation scenarios.